While thousands of proteins involved in development of the human body are capable of self-assembling in a distributed manner from merely 20 types of amino acid, macroscopic products that can be assembled spontaneously from `alive' components remains an aspiration in engineering. To attain such a mechanism, a major challenge lies in understanding which attributes from the bio-molecular realm must be leveraged at the macro-scale. Inspired by protein folding, we present a centimetre-size 1D tile chain whose self-folding processes are directed by structure-embedded magnetic interactions, which can theoretically self-assemble into convex 2D structures of any size or shape without the aid of a global `controller'. Each tile holds two magnets contained in paths designed to control their interactions. Once initiated by a magnetic unit (termed Catalyst), the chain self-reconfigures by consuming magnetic potential energy stored between magnet pairs, until the final 2D structure is reached at an energetic minimum. Both simulation and experimental results are presented to illustrate the method's efficacy on chains of arbitrary length. Results demonstrate the promise of a physically implemented, bottom-up, and scalable self-assembly method for novel 2D structure manufacturing, bridging the bio-molecular and mechanical realms.